Mass and Free Energy of Lovelock Black Holes

TL;DR

This paper derives a formula for the mass and analyzes thermodynamic properties of Lovelock black holes, revealing phase transitions and stability characteristics across different dimensions.

Contribution

It provides an explicit ADM mass formula for Lovelock black holes and explores their thermodynamics, including free energy and temperature behavior, independent of specific Lovelock couplings.

Findings

Existence of a minimum temperature for black holes in even dimensions.

Large black holes have negative free energy, indicating Hawking-Page transition.

Small black holes in odd dimensions have positive specific heat and vanishing temperature.

Abstract

An explicit formula for the ADM mass of an asymptotically AdS black hole in a generic Lovelock gravity theory is presented, identical in form to that in Einstein gravity, but multiplied by a function of the Lovelock coupling constants and the AdS curvature radius. A Gauss' law type formula relates the mass, which is an integral at infinity, to an expression depending instead on the horizon radius. This and other thermodynamic quantities, such as the free energy, are then analyzed in the limits of small and large horizon radius, yielding results that are independent of the detailed choice of Lovelock couplings. In even dimensions, the temperature diverges in both limits, implying the existence of a minimum temperature for black holes. The negative free energy of sufficiently large black holes implies the existence of a Hawking-Page transition. In odd dimensions the temperature still diverges for large black holes, which again have negative free energy. However, the temperature vanishes as the horizon radius tends to zero and sufficiently small black holes have positive specific heat.